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                <h1 id="workflow-of-parnmpc">Workflow of ParNMPC</h1>
<h2 id="preparation">Preparation</h2>
<ol>
<li>Choose a compiler that supports code generation with OpenMP by <code class="codehilite"><span class="err">mex -setup</span></code>.</li>
<li>Edit <code class="codehilite"><span class="err">Timer.m</span></code> to specify your own timer function.</li>
</ol>
<h2 id="nmpc-problem-formulation">NMPC Problem Formulation <div id="nmpc_formulation"></div></h2>
<div class="admonition example">
<p class="admonition-title">Example</p>
<p><code class="codehilite"><span class="err">./NMPC_Problem_Definition.m</span></code></p>
</div>
<ol>
<li>
<p>Formulate an OCP using Class <code class="codehilite"><span class="err">OptimalControlProblem</span></code>
<div class="codehilite"><pre><span></span><span class="c">% Create an OptimalControlProblem object</span>
<span class="n">OCP</span> <span class="p">=</span> <span class="n">OptimalControlProblem</span><span class="p">(</span><span class="n">dim</span><span class="p">.</span><span class="n">u</span><span class="p">,</span><span class="c">...  % inputs dim</span>
                            <span class="n">dim</span><span class="p">.</span><span class="n">x</span><span class="p">,</span><span class="c">...  % states dim</span>
                            <span class="n">dim</span><span class="p">.</span><span class="n">p</span><span class="p">,</span><span class="c">...  % parameters dim</span>
                            <span class="n">N</span><span class="p">);</span>        <span class="c">% num of discretization grids</span>

<span class="c">% Give names to x, u, p (optional)                          </span>
<span class="p">[</span><span class="o">~</span><span class="p">]</span> <span class="p">=</span> <span class="n">OCP</span><span class="p">.</span><span class="n">setStateName</span><span class="p">(</span><span class="o">~</span><span class="p">);</span>
<span class="p">[</span><span class="o">~</span><span class="p">]</span> <span class="p">=</span> <span class="n">OCP</span><span class="p">.</span><span class="n">setInputName</span><span class="p">(</span><span class="o">~</span><span class="p">);</span>
<span class="p">[</span><span class="o">~</span><span class="p">]</span> <span class="p">=</span> <span class="n">OCP</span><span class="p">.</span><span class="n">setParameterName</span><span class="p">(</span><span class="o">~</span><span class="p">);</span>

<span class="c">% Set the prediction horizon T </span>
<span class="n">OCP</span><span class="p">.</span><span class="n">setT</span><span class="p">(</span><span class="o">~</span><span class="p">);</span>

<span class="c">% Set the dynamic function f</span>
<span class="n">OCP</span><span class="p">.</span><span class="n">setf</span><span class="p">(</span><span class="o">~</span><span class="p">);</span>

<span class="c">% Set the matrix M (optional for, e.g., Lagrange model)</span>
<span class="n">OCP</span><span class="p">.</span><span class="n">setM</span><span class="p">(</span><span class="o">~</span><span class="p">);</span>

<span class="c">% Set the equality constraint function C (optional)</span>
<span class="n">OCP</span><span class="p">.</span><span class="n">setC</span><span class="p">(</span><span class="o">~</span><span class="p">);</span>

<span class="c">% Set the cost function L</span>
<span class="n">OCP</span><span class="p">.</span><span class="n">setL</span><span class="p">(</span><span class="o">~</span><span class="p">);</span>

<span class="c">% Set the polytopic constraint G (optional)</span>
<span class="n">OCP</span><span class="p">.</span><span class="n">setG</span><span class="p">(</span><span class="o">~</span><span class="p">);</span>

<span class="c">% Generate necessary files</span>
<span class="n">OCP</span><span class="p">.</span><span class="n">codeGen</span><span class="p">();</span>
</pre></div></p>
</li>
<li>
<p>Configure the solver using Class <code class="codehilite"><span class="err">NMPCSolver</span></code>
<div class="codehilite"><pre><span></span><span class="c">% Create a NMPCSolver object</span>
<span class="n">nmpcSolver</span> <span class="p">=</span> <span class="n">NMPCSolver</span><span class="p">(</span><span class="n">OCP</span><span class="p">);</span>

<span class="c">% Configurate the Hessian approximation method</span>
<span class="n">nmpcSolver</span><span class="p">.</span><span class="n">setHessianApproximation</span><span class="p">(</span><span class="o">~</span><span class="p">);</span>

<span class="c">% Configurate the descent regularization parameter (optional)</span>
<span class="n">nmpcSolver</span><span class="p">.</span><span class="n">setDescentRegularization</span><span class="p">(</span><span class="o">~</span><span class="p">);</span>

<span class="c">% Generate necessary files</span>
<span class="n">nmpcSolver</span><span class="p">.</span><span class="n">codeGen</span><span class="p">();</span>
</pre></div></p>
</li>
<li>
<p>Solve the very first OCP offline to provide an accurate initial guess
<div class="codehilite"><pre><span></span><span class="c">% Set the initial state</span>
<span class="n">x0</span> <span class="p">=</span> <span class="p">[</span><span class="o">~</span><span class="p">];</span>

<span class="c">% Set the parameters</span>
<span class="n">p </span><span class="s"> = [~]</span><span class="p">;</span>

<span class="c">% Create an initial guess</span>
<span class="n">solutionInitGuess</span> <span class="p">=</span> <span class="p">[</span><span class="o">~</span><span class="p">];</span>

<span class="c">% Solve the optimal control problem for given values of x0 and p </span>
<span class="c">% with barrier parameter rho</span>
<span class="n">solution</span> <span class="p">=</span> <span class="n">NMPC_SolveOffline</span><span class="p">(</span><span class="n">x0</span><span class="p">,</span><span class="n">p</span><span class="p">,</span><span class="n">solutionInitGuess</span><span class="p">,</span><span class="n">rho</span><span class="p">,</span><span class="n">maxIter</span><span class="p">);</span>


<span class="c">% Save to file for Simu_Matlab.m</span>
<span class="n">save </span><span class="s">GEN_initData.mat dim x0 p N</span><span class="p"></span>

<span class="c">% Set initial guess</span>
<span class="k">global</span> <span class="n">ParNMPCGlobalVariable</span>
<span class="n">ParNMPCGlobalVariable</span><span class="p">.</span><span class="n">solutionInitGuess</span> <span class="p">=</span> <span class="n">solution</span><span class="p">;</span>
</pre></div></p>
</li>
<li>
<p>Define the controlled plant using Class <code class="codehilite"><span class="err">DynamicSystem</span></code> (optional for simulation)
<div class="codehilite"><pre><span></span><span class="c">% Create a DynamicSystem object</span>
<span class="n">plant</span> <span class="p">=</span> <span class="n">DynamicSystem</span><span class="p">(</span><span class="n">dim</span><span class="p">.</span><span class="n">u</span><span class="p">,</span><span class="n">dim</span><span class="p">.</span><span class="n">x</span><span class="p">,</span><span class="n">dim</span><span class="p">.</span><span class="n">p</span><span class="p">);</span>

<span class="c">% Give names to x, u, p (optional)</span>
<span class="p">[</span><span class="o">~</span><span class="p">]</span> <span class="p">=</span> <span class="n">plant</span><span class="p">.</span><span class="n">setStateName</span><span class="p">(</span><span class="o">~</span><span class="p">);</span>
<span class="p">[</span><span class="o">~</span><span class="p">]</span> <span class="p">=</span> <span class="n">plant</span><span class="p">.</span><span class="n">setInputName</span><span class="p">(</span><span class="o">~</span><span class="p">);</span>
<span class="p">[</span><span class="o">~</span><span class="p">]</span> <span class="p">=</span> <span class="n">plant</span><span class="p">.</span><span class="n">setParameterName</span><span class="p">(</span><span class="o">~</span><span class="p">);</span>

<span class="c">% Set the dynamic function f</span>
<span class="n">plant</span><span class="p">.</span><span class="n">setf</span><span class="p">(</span><span class="o">~</span><span class="p">);</span>

<span class="c">% Set the matrix M (optional for, e.g., Lagrange model)</span>
<span class="n">plant</span><span class="p">.</span><span class="n">setM</span><span class="p">(</span><span class="o">~</span><span class="p">);</span>

<span class="c">% Generate necessary files</span>
<span class="n">plant</span><span class="p">.</span><span class="n">codeGen</span><span class="p">();</span>
</pre></div></p>
</li>
</ol>
<p>Configuration Table:</p>
<table>
<thead>
<tr>
<th></th>
<th>Configurable discretization method</th>
<th>Configurable Hessian approximation method</th>
</tr>
</thead>
<tbody>
<tr>
<td><code class="codehilite"><span class="err">M</span></code> enabled</td>
<td><code class="codehilite"><span class="err">&#39;Euler&#39;</span></code></td>
<td><code class="codehilite"><span class="err">&#39;GaussNewton&#39;</span></code></td>
</tr>
<tr>
<td><code class="codehilite"><span class="err">M</span></code> disabled</td>
<td>All</td>
<td>All</td>
</tr>
</tbody>
</table>
<h2 id="closed-loop-simulation">Closed-loop Simulation</h2>
<p>In order to do the closed-loop simulation for the problem defined above, two functions are provided:</p>
<ul>
<li>
<p><code class="codehilite"><span class="err">NMPC_Solve</span></code>: function of the NMPC solver. See <a href="../interfaces/#NMPC_Solve">Interfaces &gt; Functions &gt; NMPC_Solve</a>.</p>
</li>
<li>
<p><code class="codehilite"><span class="err">SIM_Plant_RK4</span></code>: one-step simulation of the controlled plant based on the 4-th order Runge-Kutta method. See <a href="../interfaces/#SIM_Plant_RK4">Interfaces &gt; Functions &gt; SIM_Plant_RK4</a>.</p>
</li>
</ul>
<h2 id="code-generation-and-deployment">Code Generation and Deployment</h2>
<h3 id="matlab">MATLAB</h3>
<p>Here, assume your closed-loop simulation is performed in <code class="codehilite"><span class="err">Simu_Matlab.m</span></code>.</p>
<div class="admonition example">
<p class="admonition-title">Example</p>
<p><code class="codehilite"><span class="err">./Simu_Matlab.m</span></code></p>
</div>
<h4 id="code-generation">Code generation</h4>
<div class="admonition example">
<p class="admonition-title">Example</p>
<p><code class="codehilite"><span class="err">./Simu_Matlab_Codegen.m</span></code></p>
</div>
<p>An executable file that performs the closed-loop simulation will be generated automatically.</p>
<h3 id="simulink">Simulink <div id="workflow_deploy_simulink"></div></h3>
<p>Here, assume your closed-loop simulation is performed in Simulink. You can call the generated C/C++ solver function <code class="codehilite"><span class="err">NMPC_Solve</span></code> directly to compute the optimal input.</p>
<h4 id="code-generation_1">Code generation</h4>
<div class="admonition example">
<p class="admonition-title">Example</p>
<p><code class="codehilite"><span class="err">./Simu_Simulink_Setup.m</span></code></p>
</div>
<ol>
<li>
<p>Define and configurate options for NMPC_Solve:
<div class="codehilite"><pre><span></span><span class="n">options</span> <span class="p">=</span> <span class="n">createOptions</span><span class="p">();</span>
</pre></div></p>
</li>
<li>
<p>Generate code:
<div class="codehilite"><pre><span></span><span class="n">NMPC_Solve_CodeGen</span><span class="p">(</span><span class="o">~</span><span class="p">,</span><span class="o">~</span><span class="p">,</span><span class="n">options</span><span class="p">);</span>
</pre></div></p>
</li>
</ol>
<h4 id="deployment">Deployment</h4>
<div class="admonition example">
<p class="admonition-title">Example</p>
<p><code class="codehilite"><span class="err">./Simu_Simulink.slx</span></code></p>
</div>
<p>This example shows how to call the generated C interface in Simulink using the <code class="codehilite"><span class="err">coder.cevel</span></code> function within a <code class="codehilite"><span class="err">MATLAB Function</span></code> block. 
You can also call the C/C++ interface using S-function.</p>
<ol>
<li>
<p>Open the Simulation Target pane in the Simulink Editor:
<strong>Simulation &gt; Model Configuration Parameters &gt; Simulation Target</strong>.</p>
</li>
<li>
<p>Add <code class="codehilite"><span class="cp">#include</span> <span class="cpf">&quot;NMPC_Solve.h&quot;</span><span class="cp"></span></code> to <strong>Insert custom C code in generated: Header file</strong>.</p>
</li>
<li>
<p>Add <code class="codehilite"><span class="err">NMPC_Solve_initialize();</span></code> to <strong>Insert custom C code in generated: Initialize function</strong>.</p>
</li>
<li>
<p>Add <code class="codehilite"><span class="err">NMPC_Solve_terminate();</span></code> to <strong>Insert custom C code in generated: Terminate function</strong>.</p>
</li>
<li>
<p>Add the following directory to <strong>Additional Build Information: Include directories</strong>:
<div class="codehilite"><pre><span></span><span class="o">./</span><span class="n">codegen</span><span class="o">/~/</span><span class="n">NMPC_Solve</span>
</pre></div></p>
</li>
<li>
<p>Add <code class="codehilite"><span class="err">NMPC_Solve.lib</span></code> (<code class="codehilite"><span class="err">NMPC_Solve.so</span></code> in linux) to <strong>Additional Build Information: Libraries</strong>.</p>
</li>
<li>
<p>Call the generated C function in a <code class="codehilite"><span class="err">MATLAB Function</span></code> block in Simulink:
<div class="codehilite"><pre><span></span><span class="n">output</span> <span class="p">=</span> <span class="n">createOutput</span><span class="p">();</span>
<span class="n">solution</span> <span class="p">=</span> <span class="n">createNonemptySolution</span><span class="p">();</span>
<span class="n">coder</span><span class="p">.</span><span class="n">ceval</span><span class="p">(</span><span class="s">&#39;NMPC_Solve&#39;</span><span class="p">,</span><span class="c">...</span>
             <span class="n">x0</span><span class="p">,</span><span class="c">...</span>
             <span class="n">p</span><span class="p">,</span><span class="c">... % (optional)</span>
             <span class="n">coder</span><span class="p">.</span><span class="n">wref</span><span class="p">(</span><span class="n">solution</span><span class="p">),</span><span class="c">...</span>
             <span class="n">coder</span><span class="p">.</span><span class="n">wref</span><span class="p">(</span><span class="n">output</span><span class="p">));</span>
</pre></div></p>
</li>
</ol>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>Alternatively, steps 1-6 can be done using the following commands.
<div class="codehilite"><pre><span></span><span class="err">Simu_Simulink</span>
<span class="err">set_param(&#39;Simu_Simulink&#39;, &#39;SimCustomHeaderCode&#39;, &#39;#include &quot;NMPC_Solve.h&quot;&#39;)</span>
<span class="err">set_param(&#39;Simu_Simulink&#39;, &#39;SimCustomInitializer&#39;, &#39;NMPC_Solve_initialize();&#39;)</span>
<span class="err">set_param(&#39;Simu_Simulink&#39;, &#39;SimCustomTerminator&#39;, &#39;NMPC_Solve_terminate();&#39;)</span>
<span class="err">set_param(&#39;Simu_Simulink&#39;, &#39;SimUserLibraries&#39;, &#39;NMPC_Solve.lib&#39;)</span>
<span class="err">set_param(&#39;Simu_Simulink&#39;, &#39;SimUserIncludeDirs&#39;, &#39;./codegen/~/NMPC_Solve&#39;)</span>
</pre></div></p>
</div>
<h2 id="accelerating-simulation-using-mex-function">Accelerating Simulation using MEX-function</h2>
<ol>
<li>
<p>Code generation</p>
<div class="admonition example">
<p class="admonition-title">Example</p>
<p><code class="codehilite"><span class="err">./Simu_Simulink_Setup.m</span></code></p>
</div>
<p>Following the code generation for Simulink procedure, MEX-function can be generated by modifying the generation target to <code class="codehilite"><span class="err">mex</span></code>:
<div class="codehilite"><pre><span></span><span class="n">NMPC_Solve_CodeGen</span><span class="p">(</span><span class="s">&#39;mex&#39;</span><span class="p">,</span><span class="s">&#39;C&#39;</span><span class="p">,</span><span class="n">options</span><span class="p">);</span>
</pre></div></p>
</li>
<li>
<p>Deployment</p>
<div class="admonition example">
<p class="admonition-title">Example</p>
<p><code class="codehilite"><span class="err">./Simu_Matlab.m</span></code></p>
</div>
<p>Modify <code class="codehilite"><span class="err">NMPC_Solve</span></code> to <code class="codehilite"><span class="err">NMPC_Solve_mex</span></code> to call the generated <code class="codehilite"><span class="err">mex</span></code> function and run.</p>
<p>MEX-function is typically slower than C code. However, it can speed up your simulation to check the closed-loop response. </p>
</li>
</ol>
                
                  
                
                
              
              
                


              
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